Question

giúp em câu b với ạ, em cảm ơn

Answer 1

\(\Delta'=\left(m-1\right)^2-m^2\ge0\Rightarrow m\le\dfrac{1}{2}\)

Theo hệ thức Viet: \(\left\{{}\begin{matrix}x_1+x_2=2\left(m-1\right)\\x_1x_2=m^2\end{matrix}\right.\)

\(x_1^2+2\left(m-1\right)x_2=15\)

\(\Leftrightarrow x_1\left(x_1+x_2\right)-x_1x_2+2\left(m-1\right)x_2=15\)

\(\Leftrightarrow2\left(m-1\right)x_1+2\left(m-1\right)x_2-m^2=15\)

\(\Leftrightarrow2\left(m-1\right)\left(x_1+x_2\right)-m^2-15=0\)

\(\Leftrightarrow4\left(m-1\right)^2-m^2-15=0\)

\(\Leftrightarrow3m^2-8m-11=0\Rightarrow\left[{}\begin{matrix}m=-1\\m=\dfrac{11}{3}>\dfrac{1}{2}\left(loại\right)\end{matrix}\right.\)